| Random forest methodology is a nonparametric, machine learning approach capable of strong performance in regression and classification problems involving complex datasets. In addition to making predictions, random forests can be used to assess the relative importance of explanatory variables. In this dissertation, we explore three topics related to random forests: tree aggregation, variable importance, and robustness. In Chapter 2, we show that the method of tree aggregation used in one popular random forest implementation can lead to biased class probability estimates and that it is often beneficial to combine the tree partitioning algorithm used in one implementation with the aggregation scheme used in another. In Chapter 3, we show that imputing missing values proir to assessing variable importance often leads to inaccurate variable importance measures. Using simulation studies, we investigate the impact on variable importance of six random-forest-based imputation techniques and find that some techniques are prone to overestimating the importance of variables whose values have been imputed, while other techniques tend to underestimate the importance of such variables. In Chapter 4, we propose a new robust approach for random forest regression. Adapted from a popular approach used in polynomial regression, our method uses residual analysis to modify the weights associated with training cases in random forest predictions, so that outlying training cases have less impact. We show, using simulation studies, that this approach outperforms existing robust techniques on noisy, contaminated datasets. |
